Republicans hold the majority over Democrats in both chambers. Some Republicans opposed the measure, and others supported it -- and said they did so with reluctance.

House Speaker Jase Bolger released a statement saying the House vote today was about protecting "Michigan taxpayers and families from a massive and unwelcome federal overreach."

The vote means the state would accept nearly $31 million in federal money to set up the exchange.

From Bolger's statement:

"While accepting the planning grant may be politically unpopular with some, it is the best remaining option to help Michigan’s residents. Because of the protections we put in place as a condition for accepting the federal money, Michigan can now plan on how we can have some say over the way health care is offered to our families here."

Open enrollment in the health care exchange is set to begin on October 1st, 2013.